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    An experimental study of MR dampers for seismic protection

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    1998 Smart Mater. Struct. 7 693

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    Smart Mater. Struct. 7 (1998) 693703. Printed in the UK PII: S0964-1726(98)96181-X

    An experimental study of MR

    dampers for seismic protection

    S J Dyke, B F Spencer Jr, M K Sain and J D Carlson

    Department of Civil Engineering, Washington University, St Louis, MO 63130,

    USA Department of Civil Engineering and Geological Science, University of NotreDame, Notre Dame, IN 46556, USA Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN46556, USAMechanical Products Division, Lord Corporation, Cary, NC 27511, USA

    Received 13 March 1997, accepted for publication 23 June 1997

    Abstract. In this paper, the efficacy of magnetorheological (MR) dampers forseismic response reduction is examined. To investigate the performance of the MRdamper, a series of experiments was conducted in which the MR damper is used inconjunction with a recently developed clipped-optimal control strategy to control athree-story test structure subjected to a one-dimensional ground excitation. Theability of the MR damper to reduce both peak responses, in a series of earthquaketests, and rms responses, in a series of broadband excitation tests, is shown.

    Additionally, because semi-active control systems are nonlinear, a variety ofdisturbance amplitudes are considered to investigate the performance of this controlsystem over a variety of loading conditions. For each case, the results for threeclipped-optimal control designs are presented and compared to the performance oftwo passive systems. The results indicate that the MR damper is quite effective forstructural response reduction over a wide class of seismic excitations.

    1. Introduction

    In the last three decades or so, there has been a great deal of

    interest in the use of control systems to mitigate the effects

    of dynamic environmental hazards such as earthquakes and

    strong winds on civil engineering structures. A variety of

    control systems have been considered for these applications

    that can be classified as either passive, active, semi-active

    or hybrid (combinations of the previous types). Passive

    control systems, such as viscoelastic dampers, tuned mass

    dampers, frictional dampers, tuned liquid dampers and

    base-isolation systems, were developed as a means of

    augmenting the damping in a structure [30]. Passive

    systems impart forces on the structure by reacting to

    the localized motion of the structure, primarily acting to

    dissipate the vibratory energy in the structural system.

    These systems are now widely accepted as a viable means

    of reducing the responses of a structure. However, passive

    systems are limited because they cannot adapt to varying

    loading conditions. Thus, passive systems may performwell subjected to the loading conditions for which they were

    designed, but may not be effective in other situations.

    To develop a more versatile alternative, the concept

    of active control was introduced by Yao in 1972 [38].

    Active control systems operate by using external energy

    supplied by actuators to impart forces on the structure,

    generally depending on a sizeable power supply. The

    appropriate control action is typically determined based

    on measurements of the structural responses and/or the

    disturbance. Because the control forces are not entirely

    dependent on the local motion of the structure (although

    there is some dependence on the local response due to

    the effects of controlstructure interaction), the control

    systems are considerably more flexible in their ability to

    reduce the structural responses for a wide variety of loading

    conditions. Extensive research has been done on active

    structural control [1623, 29], and these systems have been

    installed in over twenty commercial buildings and more

    than ten bridges (during construction) [16,23]. However,

    there are still a number of questions that must be addressed

    before this technology is widely accepted, including

    questions of stability, cost effectiveness, reliability,

    power requirements etc. For instance, active systems

    have the ability to input mechanical energy into the

    structural system, making them capable of generating

    instabilities due to unmodeled dynamics and nonlinearities,

    or equipment failure (e.g., power source, sensors, control

    hardware/software etc). Additionally, the need for sizeablepower supplies and large control forces may make them

    quite costly to install and maintain.

    Semi-active systems offer another alternative in

    structural control. A variety of semi-active control devices

    have been proposed, including variable orifice dampers,

    variable friction devices, adjustable tuned liquid dampers

    and controllable fluid dampers. These systems have

    attracted much attention recently because they possess the

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    adaptability of active control systems, yet are intrinsically

    stable and operate using very low power. Typically, a

    semi-active control device is defined as one that cannot

    increase the mechanical energy in the controlled system

    (i.e., including both the structure and the device), but

    has properties that can be dynamically varied. Because

    these devices are adaptable, they are expected to be quite

    effective for structural response reduction over a wide range

    of loading conditions. Additionally, semi-active control

    devices do not require large power sources such as those

    associated with active control systems, making them quite

    attractive for seismic applications. Moreover, semi-activedevices are inherently stable (in a bounded inputbounded

    output sense), which makes it possible to implement high

    authority control strategies which, in practice, may result

    in performances that can surpass that of comparable active

    systems.

    One semi-active device that appears to be particularly

    promising for seismic protection is the magnetorheological

    (MR) damper [4, 5, 1115,3234]. MR dampers use MR

    fluids to produce controllable dampers. MR fluids are

    the magnetic analogs of electrorheological (ER) fluids

    [17,18, 25, 27, 28, 36], and, like ER fluids, the essential

    characteristic of the MR fluids is their ability to reversibly

    change from a free-flowing, linear viscous fluid to a semi-

    solid in milliseconds when exposed to a magnetic field (or

    in the case of ER fluids, an electric field). A typical MR

    fluid consists of 2040% by volume of relatively pure,

    soft iron particles, e.g. carbonyl iron, suspended in an

    appropriate carrier liquid such as mineral oil, synthetic

    oil, water or a glycol. Particle diameter is typically 3

    to 5 microns. A variety of proprietary additives similar

    to those found in commercial lubricants are commonly

    added that discourage gravitational settling and promote

    particle suspension, enhance lubricity, modify viscosity

    and inhibit wear. The ultimate strength of a MR fluid

    depends on the square of the saturation magnetization of

    the suspended particle [3,5, 19, 20], and the key to a strong

    MR fluid is to choose a particle with a large saturationmagnetization. Pure iron particles, the best practical choice,

    have a saturation magnetization of 2.15 T [5] and MR fluids

    made from iron particles exhibit a yield strength of 50

    100 kPa for an applied magnetic field of 150250 kA m1.

    Although the characteristics of MR and ER fluids

    are similar in some respects, devices which are based

    on MR fluids appear to have a number of advantages,

    making them extremely promising for civil engineering

    applications [1, 2]. For example, the achievable yield stress

    of MR fluids is an order of magnitude greater than its ER

    counterpart, making it possible to develop devices which

    are capable of generating larger forces. Additionally, MR

    fluids are not highly sensitive to contaminants or impuritiessuch as are commonly encountered during manufacture

    and usage. Further, because the magnetic polarization

    mechanism is not affected by the surface chemistry of

    surfactants and additives, it is relatively straightforward

    to stabilize MR fluids against particleliquid separation

    in spite of the large density mismatch. Antiwear and

    lubricity additives can also be included in the formulation

    without affecting strength and power requirements. Devices

    employing the MR fluid can be controlled with a low power

    (e.g., less than 50 watts), low voltage (e.g., 1224 V),

    current-driven power supply outputting only 12 amps,

    which could be readily supplied by batteries. MR fluids

    have been used to develop semi-active control devices

    for a variety of applications, including braking devices

    in exercise equipment, and actuators in vehicular seat

    suspension systems [14]. MR fluid technology appears

    to be scalable to the size required for seismic control

    applications. To demonstrate the feasibility of producing

    forces required for full-scale structures, Lord Corporation

    has recently designed and built a 20 ton MR damper.Testing on the full-scale MR damper is currently under way

    at the University of Notre Dame [4, 5].

    Because MR dampers are intrinsically nonlinear, one of

    the challenges is to develop appropriate control algorithms

    to take advantage of the unique characteristics of the

    device. Various approaches have been proposed in the

    literature for the control of semi-active systems (see,

    for example, [12,13, 24,25, 28]). To be implementable,

    the algorithms must use readily available measurements,

    such as accelerations, in determining the control action.

    Previously, a number of active control experiments have

    been conducted to demonstrate the efficacy of acceleration

    feedback control strategies based on H2/LQG techniques

    [7, 9, 10, 13]. For semi-actively controlled structures, Dyke

    et al [1115] have extended these results to develop

    a clipped-optimal control strategy based on acceleration

    feedback, and shown the effectiveness of this approach.

    The focus of this paper is to experimentally demonstrate

    the ability of the MR damper to reduce structural responses

    over a wide range of loading conditions. Following a

    description of the experimental setup, the procedure used

    to identify a model of the integrated MR damper/structure

    is described. A clipped-optimal control algorithm, recently

    developed for use with the MR damper [1115], is then

    discussed. In the experiments, the ability of the system

    to reduce both the peak responses, in the case of the

    earthquake excitation, and rms response, in the case ofthe broadband excitation, is studied. Due to the intrinsic

    nonlinear behavior of the MR damper, the performance of

    the control system will vary with the magnitude of the

    disturbance. Thus, the amplitude of the disturbance was

    also varied in the tests. The performance of the semi-

    actively controlled structure is compared to that of two

    cases in which the MR damper is used in a passive mode,

    designated passive-off and passive-on. The results reported

    herein indicate that this semi-active control system is quite

    effective for seismic response reduction over a wide range

    of seismic excitations.

    2. Experimental setup

    Figure 1 is a diagram of the semi-actively controlled,

    three-story, model building at the Structural Dynamics

    and Control/Earthquake Engineering Laboratory at the

    University of Notre Dame (http://www.nd.edu/quake/).

    The test structure used in this experiment is designed to

    be a scale model of the prototype building discussed in

    Chung et al [6] and is subjected to a one-dimensional

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    Figure 1. Diagram of MR damper implementation.

    Figure 2. Schematic of MR damper.

    ground motion. The building frame is constructed of steel,

    with a height of 158 cm. The floor masses of the model

    weigh a total of 227 kg, distributed evenly between the

    three floors. The time scale factor is 0.2, making the natural

    frequencies of the model approximately five times those ofthe prototype. More information on this test structure is

    available in [35].

    In this experiment, a single magnetorheological (MR)

    damper is installed between the ground and the first floor,

    as shown in figure 1. The MR damper employed here is a

    prototype device, shown schematically in figure 2, obtained

    from the Lord Corporation for testing and evaluation [33]

    (see also http://www.mrfluid.com). The damper is 21.5 cm

    long in its extended position and has a 2.5 cm stroke.

    The main cylinder is 3.8 cm in diameter and houses the

    piston, the magnetic circuit, an accumulator and 50 ml

    of MR fluid. The magnetic field produced in the device

    is generated by a small electromagnet in the piston head.The current for the electromagnet is supplied by a linear

    current driver which generates a current that is proportional

    to the applied voltage. The peak power required is less than

    10 watts. The system, including the damper and the current

    driver, has a response time of typically less than 10 ms.

    A number of sensors are installed in the model building

    for use in determining the control action. Accelerometers

    located on each of the three floors provide measurements

    Figure 3. Simple mechanical model of the MR damper.

    of the absolute accelerations, xa1 xa2 xa3, an LVDT (linear

    variable differential transformer) measures the displacement

    xd of the MR damper, and a force transducer is placed in

    series with the MR damper to measure the control force

    f being applied to the structure. Note that only these five

    measurements are used in the control algorithm. However,

    to evaluate the performance of the control strategies, LVDTs

    are attached to the base and to each floor of the structure

    to measure the relative displacements of the structure.

    Implementation of the discrete controller was per-

    formed using the Spectrum Signal Processing Real-TimeDigital Signal Processor (DSP) System. A discussion of

    the specific capabilities of this board which make it suit-

    able for use in structural control systems is provided in

    Quast et al [37].

    3. System identification

    One of the most important and challenging tasks in

    control synthesis and analysis is the development of an

    accurate mathematical model of the structural system

    under consideration, including both the structure and theassociated control devices. The approach to system

    identification of semi-actively controlled structures outlined

    in [32] is employed. In this approach, the problem is

    simplified by decoupling the identification of the nonlinear

    semi-active device from that of the primary structure. If the

    semi-active controller is assumed to be adequate to keep the

    response of the primary structure in the linear range, then

    standard linear system identification techniques can be used

    to develop a model for the primary structure. Nonlinear

    identification means must still be employed to identify the

    semi-active control device. Additionally, this approach

    is attractive because the identification of the semi-active

    system requires only measurements which are available for

    controlling the responses of the structure.

    The approach consists of four steps: (i) modeling

    and identification of the semi-active control device, (ii)

    identification of a model of the primary structure, (iii)

    integration and optimization of the device and structural

    models and (iv) validation of the integrated model of the

    system. These steps are briefly described in the subsequent

    sections.

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    Figure 4. Comparison of the model results and the experimental data for the random displacement, random voltage test.

    3.1. Modeling and identification of the MR damper

    The first step in the identification process is to develop

    an input/output model for the MR damper. The simple

    mechanical idealization of the MR damper depicted in

    figure 3 has been shown to accurately predict the behavior

    of a prototype MR damper over a broad range of inputs

    [31, 33]. The equations governing the forcef predicted by

    this model are given by

    f =c1y+ k1

    xd x0

    (1)

    z= |xd y|z|z|n1

    xd t

    |z|n +A

    xd y

    (2)

    y =1

    c0+ c1z+c0xd+ k0xd y (3)

    where z is an evolutionary variable that accounts for the

    history dependence of the response. The model parameters

    depend on the voltage v to the current driver as follows

    = a + bu c1 = c1a+ c1bu c0 = c0a + c0bu

    (4)

    whereu is given as the output of the first-order filter

    u= (uv). (5)

    Equation (5) is necessary to model the dynamics involved

    in reaching rheological equilibrium and in driving the

    electromagnet in the MR damper [31, 33].A nominal set of parameters was obtained based on the

    response of the MR damper in a series of displacement-

    controlled tests. A hydraulic actuator was employed to

    drive the MR damper, and the displacement and force

    generated in the MR damper were measured, as described

    in [31, 33]. A typical response of the MR damper for

    a sinusoidal input is shown in figure 4. A least-squares

    output-error method was employed in conjunction with a

    constrained nonlinear optimization to obtain the 14 modelparameters in equations (1)(5). The optimization was

    performed using the sequential quadratic programming

    algorithm available in MATLAB [26]. A representative

    comparison of the response predicted by this model and

    the experimentally measured response for the MR damper

    is shown in figure 4. The resulting parameters were used to

    initialize the identification of the integrated system model,

    presented subsequently.

    3.2. Identification of the primary structure

    The next step in identifying a model of the integrated

    system is to develop an input/output model of the

    structure. Because the structure itself is assumed to

    remain in the linear region, the frequency domain approach

    to linear system identification discussed in Dyke et al

    [7, 9, 10, 13] and Spencer and Dyke [32] is used to identify

    a mathematical model of the test structure.

    A block diagram of the structural system to be identified

    is shown in figure 5. There are two inputs to the structural

    system, including the ground excitation xg and the applied

    control forcef. The four measured system outputs are the

    displacement xd of the structure at the attachment point

    of the MR damper, and the absolute accelerations, xa1,

    xa2, xa3, of the three floors of the test structure (i.e.,

    y = [xdxa1 xa2 xa3]). Thus, a 4 2 transfer function

    matrix must be identified to describe the characteristics ofthe system in figure 5.

    The first step in the identification of the structure is to

    experimentally determine the transfer functions from each

    of the system inputs to each of the outputs. The eight

    transfer functions are determined by independently exciting

    each of the inputs of the structure with a random input and

    measuring the structural responses. The transfer functions

    from the ground acceleration to each of the measured

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    Figure 5. System identification block diagram.

    responses were obtained by exciting the structure with a

    band-limited white noise ground acceleration (050 Hz).

    During this test, the MR damper is not connected to the

    structure, thus making f = 0. Similarly, the experimental

    transfer functions from the applied control force to each

    of the measured outputs are determined. To this end,

    the MR damper is replaced with a hydraulic actuator to

    apply a band-limited white noise (05 Hz) force to the

    structure while the base of the structure is held fixed. The

    force transducer, mentioned previously, is placed in series

    with the hydraulic actuator to directly measure the applied

    force. A representative transfer function from the ground

    acceleration to the third floor absolute acceleration is shownin figure 6. This transfer function was obtained using

    twenty averages. The three distinct, lightly damped peaks

    occurring at 5.88, 17.5 and 28.3 Hz correspond to the first

    three modes of the structural system.

    Once the experimental transfer functions have been

    obtained, the next step in the system identification

    procedure is to model each transfer function as a ratio

    of two polynomials in the Laplace variable s. This

    task is accomplished via a least-squares fit of the ratio

    polynomials, evaluated on the jaxis, to the experimentally

    obtained transfer functions. For this structure, the decision

    was made to focus control efforts on reducing the structural

    responses in the first three modes. Thus, the model isrequired to be accurate below 35 Hz. Six poles are

    necessary to model the input/output behavior of each of

    the transfer functions in the frequency range of interest.

    The system is then assembled in state space form using

    the analytical representation of the transfer functions (i.e.,

    the poles, zeros and gain). Because all of the transfer

    functions required six states, the combined system has a

    total of twelve poles. A model reduction is performed

    to achieve a minimal realization of the system; thus, the

    twelve-state system was reduced to a six-state system,

    resulting in a reduced-order model of the form

    xr = Axr + Bf +Exg

    y = Cyxr + Dyf + v(6)

    wherev represents the measurement noise vector.

    A representative comparison of the reduced-order

    model to the experimental transfer functions is shown in

    figure 6. Additional details regarding this frequency domain

    identification approach can be found in Dyke et al [7

    10,13].

    3.3. Development of an integrated system model

    The next step in identifying a model of the integrated

    structural system is to optimize the set of parameters for the

    MR damper model (equations (1)(5)) for the case when it

    is installed in the test structure, and combine the models

    of the device and structure to form the integrated system

    model (shown in figure 7). Updating the parameters of the

    MR damper model is necessary because the MR damper

    may function at a different operating point when installed

    in the test structure than in the initial tests in which the

    damper was driven with a hydraulic actuator [32].

    To update the parameters of the MR damper model, a

    series of tests was conducted to measure the response of the

    structure with the MR damper in place in the test structure

    (see figure 1). In these tests, the structure was excited at the

    base, while various voltages v were applied to the current

    driver of the MR damper. The recorded system responses

    included the force generated in the MR damper, absolute

    accelerations of each floor, displacement of the floors of

    the structure, displacement of the base and displacement

    of the three floors of the structure. Optimized parameters

    were determined to fit the generalized model of the MR

    damper to the experimental data. The resulting parameters

    are: c0a = 8 N s cm1, c0b = 6 N s cm

    1 V1, k0 =

    50 N cm1, c1a = 290 N s cm1, c1b = 5 N s cm1 V1,k1 = 12 N cm

    1, x0 = 14.3 cm, a =100, b = 450 V1,

    = 363 cm2, = 363 cm2, A = 301, n = 2,

    = 190 s1.

    The integrated system model is then formed by

    connecting the models of the MR damper (equations (1)

    (5)) and structure (equation (6)) as shown in figure 7.

    Verification of this integrated system model is provided in

    the following section.

    3.4. Experimental validation of the integrated system

    model

    To verify that the identified model is adequate forcontrol synthesis and analysis, the predicted response and

    experimental response were compared in one controlled

    case (controller A as described in the following section).

    A representative comparison of the experimental and

    predicted responses for the relative displacement and

    absolute acceleration of the third floor is shown in figure 8

    for a broadband excitation (020 Hz) with an rms ground

    acceleration of 0.20 g . Good agreement is obtained.

    4. Clipped-optimal control algorithm

    One of the main challenges in semi-active control is

    the development of an appropriate control algorithmthat can take advantage of the features of the control

    device to produce an effective control system. An

    important requirement of the control algorithm is that

    it be implementable in full-scale applications. To

    be implementable, the algorithm should use available

    measurements, such as accelerations, in determining the

    control action. Dykeet al [11, 12] have proposed a clipped-

    optimal control strategy based on acceleration feedback for

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    Figure 6. Comparison of reduced-order model and experimental transfer function: ground accelertion to third floor absoluteacceleration.

    Figure 7. Block diagram of the identified integrated structural system.

    Figure 8. Experimental and predicted responses of the semi-actively controlled system (controller A): third floor relativedisplacement and absolute acceleration.

    the MR damper. Analytical studies demonstrated that the

    MR damper, used in conjunction with the clipped optimal-

    control algorithm, was effective for controlling a multi-

    story structure with a single MR damper. In this section, the

    approach to the design of the clipped-optimal controller is

    provided. The discussion of the control algorithm considers

    the general case in which there are multiple devices present

    to control the structure, although in this experiment only a

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    single MR damper is employed.

    In the clipped-optimal controller, the approach is to

    appendn force feedback loops to induce each MR damper

    to produce approximately a desired control force. The

    desired control force of the i th MR damper is denoted fci .

    A linear optimal controller Kc(s) is designed that calculates

    a vector of desired control forces, fc = [fc1fc2. . . f cn],

    based on the measured structural response vector y and the

    measured control force vector f, i.e.,

    fc = L1

    Kc(s)Ly

    f (7)where L{} is the Laplace transform. Although the

    controllerKc(s) can be obtained from a variety of synthesis

    methods, H2/LQG strategies are advocated herein because

    of the stochastic nature of earthquake ground motions

    and because of their successful application in other civil

    engineering structural control applications [7, 9, 10, 13].

    To discuss the algorithm used for determining the

    control action, consider the i th MR damper used to control

    the structure. Because the response of the MR damper

    is dependent on the relative structural displacements and

    velocities at the point of attachment of the MR damper, the

    force generated by the MR damper cannot be commanded;

    only the voltage vi applied to the current driver of theith MR damper can be directly controlled. To induce the

    MR damper to generate approximately the corresponding

    desired optimal control force fci , the command signal vi is

    selected as follows. When thei th MR damper is providing

    the desired optimal force (i.e.,fi =fci ), the voltage applied

    to the damper should remain at the present level. If the

    magnitude of the force produced by the damper is smaller

    than the magnitude of the desired optimal force and the

    two forces have the same sign, the voltage applied to the

    current driver is increased to the maximum level so as to

    increase the force produced by the damper to match the

    desired control force. Otherwise, the commanded voltage

    is set to zero. The algorithm for selecting the command

    signal for the i th MR damper is graphically represented infigure 9 and can be concisely stated as

    vi =VmaxH

    fci fi

    fi

    (8)

    where Vmax is the voltage to the current driver associated

    with saturation of the MR effect in the tested device, and

    H () is the Heaviside step function. A block diagram of

    this semi-active control system is shown in figure 10. In the

    block diagram, the dependence of the MR damper forces on

    the structural responses is indicated by the link feeding back

    the vectors xr and xr , which contain the relative structural

    displacements and velocities at the attachment points of

    the MR damper. For instance, if three MR dampers were

    rigidly attached between the first three floors of a structure,this vector would be xr =[x1x2x1x3 x2]

    .

    One of the attractive features of this control strategy

    is that the feedback for the controller is based on readily

    obtainable acceleration measurements, thus making them

    quite implementable. In addition, the proposed control

    design does not require a model for the MR damper,

    although the model of the damper is important to system

    analysis.

    Figure 9. Graphical representation of algorithm forselecting the command signal.

    Figure 10. Block diagram of the semi-active controlsystem.

    5. Experimental results

    To evaluate the performance of the semi-active control

    system employing the MR damper, eight controllers with

    various performance objectives were designed based on

    the identified model of the integrated structure/MR damper

    system and implemented in the laboratory. The results

    of three semi-active control designs, denoted AC, are

    presented herein. Controller A was designed by placing

    a high weighting on the third floor relative displacement.

    Controllers B and C were designed by placing a low and

    high weighting, respectively, on the third floor acceleration.

    In the results, xi is the displacement of thei th floor relative

    to the ground, di is the interstory drift (i.e., xi xi1), xaiis the absolute acceleration of the ith floor and f is the

    measured control force.

    In addition to the results for semi-active controllers, two

    passive cases are considered. Passive-off and passive-on

    refer to the cases in which the voltage to the MR damper is

    held at a constant value ofV =0 and V =Vmax = 2.25 V,respectively. Theuncontrolled response refers to the case

    in which the MR damper is not attached to the structure.

    Two types of experiment were conducted to evaluate

    the performance of the control designs. In the first set of

    tests, the three-story model structure was subjected to a

    scaled 1940 El Centro earthquake and the peak values of

    the measured responses were determined. In these tests,

    the earthquake was reproduced at five times the recorded

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    speed to satisfy the similitude relations. In the second set

    of tests, the three-story model structure was subjected to a

    200 second broadband signal (020 Hz) and rms values of

    the measured responses were calculated.

    Because the MR damper is a nonlinear device, its

    performance will vary for different excitation levels. Thus,

    the earthquake tests were performed at two different

    excitation amplitudes (80% and 120% of the recorded El

    Centro earthquake) and the broadband tests were conducted

    at three different input amplitudes including excitations

    with rms values of 0.06 g (low), 0.13 g (medium) and

    0.20g (high).Because in some cases the excitation levels used in

    the passive and controlled tests were quite large for the

    test structure, exciting the uncontrolled structure with the

    same excitation could have been destructive. Therefore,

    the uncontrolled results presented herein were obtained

    by using an excitation with 50% of that used in the

    controlled tests, and then scaling the uncontrolled structural

    responses up to represent the response of the structure to

    the full excitation. Thus the uncontrolled results represent

    the response of the structure if it were to remain linear

    throughout the tests.

    The experimental results are summarized in the

    following sections.

    5.1. El Centro earthquake results

    Table 1 summarizes the results of the high and low

    amplitude El Centro earthquake excitation tests. Notice

    that both the passive-off and passive-on systems are able

    to achieve a reasonable level of performance at high and

    low excitation levels. Because the MR damper is capable of

    generating larger damping forces in the passive-on case than

    in the passive-off case, one might predict that the passive-

    on system would achieve larger reductions in the responses.

    However, from the results it is shown that a number of

    the responses of the passive-on system are actually larger

    than those of the passive-off system. For instance, in the

    low amplitude tests, the third floor displacement, maximum

    interstory displacement and maximum floor acceleration

    of the passive-on system are 11.3%, 10.9% and 19.0%

    larger, respectively, than the responses of the passive-

    off system. In the high amplitude tests, the passive-on

    controller performs better than the passive-off controller in

    reducing the peak third floor displacement and maximum

    interstory displacement, but an increase in the absolute

    accelerations is still observed.

    The results presented in table 1 show that all of the

    semi-active control systems perform significantly better

    than the passive systems. In the high amplitude tests,

    controller A achieves a 24.3% reduction in the peak

    third floor displacement and a 29.1% reduction in themaximum interstory displacement over the best passive

    responses. Furthermore, these reductions were obtained

    while achieving a modest reduction in the maximum

    acceleration. Additional reduction in the peak third floor

    relative displacement over the best passive case is achieved

    with controller C (33.3%), although with an increase in the

    maximum acceleration. Notice that for all of the semi-

    actively controlled systems, these performance gains are

    achieved while requiring significantly smaller control forces

    than are required in the passive-on case.

    At low excitation amplitudes, the performance of

    the semi-active controllers is still superior to that of

    the passive controllers, although not to as great an

    extent. The third floor relative displacement, maximum

    interstory displacement and maximum absolute acceleration

    are reduced over the best passive case by 11.3%, 27.8%

    and 3.6%, respectively, with controller A. Again, additional

    reduction in the third floor relative displacement is achieved

    with controllers B (20%) and C (23.3%), although the

    maximum acceleration response is increased in these cases.Figure 11 shows the uncontrolled and semi-actively

    controlled (using controller A) responses for the tested

    structure. The effectiveness of the proposed control strategy

    is clearly seen, with peak third floor displacement being

    reduced by 74.5% and the peak third floor acceleration

    being reduced by 47.6% over the uncontrolled responses.

    5.2. Random excitation results

    The rms values of the structural responses in the random

    excitation test are provided in table 2. Here, the passive

    systems are able to achieve reasonable reduction in the

    structural responses at all excitation levels. In the high

    amplitude tests, most of the rms responses of the passive-

    on system are better than those of the passive-off system.

    However, at lower excitation levels, the rms responses of

    the passive-on system are often larger than those of the

    passive-off system. For instance, in both the low and

    medium amplitude tests, the maximum rms acceleration

    is larger in the passive-on case than in the passive-off

    case. Additionally, in the low amplitude test, the maximum

    interstory displacement is 25% larger in the passive-on case

    than in the passive-off case. This demonstrates that using a

    passive device which is capable of generating large control

    forces is not always the best approach.

    The results indicate that the semi-active control systems

    perform significantly better at reducing the rms structuralresponses than the passive systems. At all excitation

    levels, the three semi-active controllers are able to reduce

    not only the rms third floor relative displacements and

    interstory displacements, but also the maximum rms floor

    accelerations, well below those obtained with the passive

    systems. Controller B achieves the best performance of

    the three semi-active control designs, reducing the third

    floor displacement, maximum interstory displacement and

    the maximum floor absolute acceleration, by 14.6%, 26.5%

    and 23.6%, respectively, over the best passive case in the

    high amplitude tests, and by 17.8%, 30.0% and 8.0% in

    the medium amplitude tests. Even at low amplitudes, a

    modest reduction in the structural responses is observed.

    Again, notice that the semi-active controllers achieve these

    performance levels while using significantly less force than

    the passive-on system.

    6. Conclusion

    The efficacy of the MR damper in reducing the structural

    responses for a wide range of loading conditions has been

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    Table 1. Experimental peak responses due to the El Centro earthquake.

    Clipped-optimal Clipped-optimal Clipped-optimalUncontrolled Passive-off Passive-on controller A controller B controller C

    High amplitude: responses due to the 120% El Centro earthquakexi 0.710 0.236 0.126 0.127 0.157 0.151(cm) 1.068 0.362 0.312 0.229 0.264 0.213

    1.249 0.436 0.420 0.318 0.335 0.280

    di 0.710 0.236 0.126 0.127 0.157 0.151(cm) 0.362 0.167 0.196 0.139 0.139 0.123

    0.205 0.106 0.110 0.092 0.081 0.087

    xai 879 666 920 711 874 957(cm s2) 1110 714 808 642 673 859

    1500 804 897 786 653 748

    xd (cm) 0.214 0.095 0.112 0.133 0.133

    f (N) 258 1030 696 668 754

    Low amplitude: responses due to the 80% El Centro earthquakexi 0.473 0.119 0.074 0.084 0.087 0.089(cm) 0.712 0.197 0.196 0.157 0.148 0.136

    0.833 0.240 0.267 0.213 0.192 0.184

    di 0.473 0.119 0.074 0.084 0.087 0.089(cm) 0.241 0.099 0.132 0.086 0.085 0.077

    0.137 0.067 0.083 0.066 0.060 0.059

    xai 586 388 595 462 542 657(cm s2) 740 481 546 457 579 759

    1000 500 594 482 521 545

    xd (cm) 0.112 0.049 0.063 0.071 0.071

    f (N) 224 768 537 580 630

    Figure 11. Controlled and uncontrolled structural responses due to 120% El Centro earthquake (controller A).

    demonstrated in a series of experiments conducted at the

    Structural Dynamics and Control/Earthquake EngineeringLaboratory at the University of Notre Dame. In these

    experiments, the MR damper was used in conjunction

    with a clipped-optimal control algorithm to control the

    responses of a three-story test structure. The clipped-

    optimal control algorithm is implementable in that it uses

    readily available measurements of the structural responses,

    primarily absolute accelerations, to perform the control

    calculations.

    The MR damper was shown to effectively reduce both

    the peak and rms responses due to a broad class of seismicexcitations. Three different clipped-optimal control designs

    were considered, and each of the control designs achieved

    excellent results. In all cases, the semi-active controllers

    performed significantly better than both of the passive

    systems considered in reducing the structural responses.

    Reductions in both acceleration and displacement responses

    were observed with the semi-actively controlled systems.

    Additionally, the semi-active control systems were able

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    Table 2. Experimental rms responses due to the random excitations.

    Clipped-optimal Clipped-optimal Clipped-optimalUncontrolled Passive-off Passive-on controller A controller B controller C

    High amplitude: responses to the high amplitude random excitationxi 0.250 0.070 0.027 0.036 0.036 0.038(cm) 0.382 0.112 0.070 0.066 0.065 0.066

    0.467 0.139 0.103 0.091 0.088 0.089

    di 0.250 0.070 0.027 0.036 0.036 0.038(cm) 0.156 0.048 0.049 0.039 0.036 0.036

    0.123 0.035 0.036 0.031 0.027 0.029

    xai 1020 274 226 228 209 225(cm s2) 576 184 178 159 153 176

    999 292 292 250 223 241

    xd (cm) 0.066 0.020 0.033 0.032 0.034

    f (N) 112 311 219 209 220

    Medium amplitude: responses to the medium amplitude random excitationxi 0.164 0.036 0.018 0.022 0.022 0.023(cm) 0.248 0.059 0.049 0.043 0.043 0.044

    0.304 0.077 0.073 0.062 0.060 0.061

    di 0.163 0.036 0.018 0.022 0.022 0.023(cm) 0.101 0.028 0.035 0.028 0.026 0.027

    0.080 0.022 0.026 0.022 0.020 0.021

    xai 663 168 162 154 149 161(cm s1) 374 112 134 115 113 126

    649 176 208 174 162 172

    xd (cm) 0.031 0.010 0.018 0.019 0.020

    f (N) 105 237 174 161 170

    Low amplitude: responses to the low amplitude random excitationxi 0.075 0.013 0.009 0.009 0.010 0.010(cm) 0.115 0.026 0.026 0.024 0.023 0.023

    0.140 0.035 0.037 0.034 0.033 0.033

    di 0.075 0.013 0.009 0.009 0.010 0.010(cm) 0.047 0.016 0.020 0.017 0.016 0.017

    0.037 0.012 0.014 0.012 0.012 0.012

    xai 306 88.3 114 102 102 105(cm s1) 173 68.3 88.1 78.3 76.8 78.7

    300 92.5 113 102 95.6 96.9

    xd (cm) 0.017 0.007 0.010 0.012 0.014

    f (N) 85.0 140 121 111 113

    to achieve these performance gains while using smaller

    control forces than in the passive-on system. Moreover,

    the capabilities of the MR damper have been shown to

    mesh well with the requirements and constraints associated

    with the seismic response reduction in civil engineering

    structures.

    Note that algorithms that explicitly incorporate actuator

    dynamics and controlstructure interaction into the control

    design process may offer additional controlled performance

    gains [8]. Efforts are currently under way to investigate this

    possibility.

    Acknowledgment

    This research is supported in part by National Science

    Foundation grant Nos CMS 93-01584 and CMS 95-00301.

    In addition, the authors from Notre Dame and Washington

    University would like to express their appreciation to

    Lord Corporation of Cary, NC for providing the prototype

    magnetorheological damper.

    References

    [1] Carlson J D 194 The promise of controllable fluids Proc.Actuator 94 ed H Borgmann and K Lenz (AXON)pp 266-70

    [2] Carlson J D and Weiss K D 1994 A growing attraction tomagnetic fluids Machine Design Aug pp 61-4

    [3] Carlson J D and Weiss K D 1995 Magnetorheologicalmaterials based on alloy particles US Patent5 382 373

    [4] Carlson J D and Spencer B F Jr 1996 Magneto-rheologicalfluid dampers for semi-active seismic control Proc. 3rdInt. Conf. on Motion and Vibration Control (Chiba,1996)vol 3 eds K Nonami and T Mizuno pp 3540

    [5] Carlson J D and Spencer B F Jr 1996 Magneto-rheologicalfluid dampers: scalability and design issues forapplication to dynamic hazard mitigation Proc. 2nd Int.Workshop on Structural Control (Hong Kong, 1996)pp 99109

    702

  • 8/14/2019 An Experimental Study of MR

    12/12

    MR dampers for seismic protection

    [6] Chung L L, Lin R C, Soong T T and Reinhorn A M 1989Experiments on active control for MDOF seismicstructures J. Eng. Mech. ASCE115 160927

    [7] Dyke S J, Spencer B F Jr, Quast P, Sain M K, Kaspari DC Jr and Soong T T 1994 Experimental verification ofacceleration feedback control strategies for an activetendon system National Center for EarthquakeEngineering Research Technical Report NCEER-94-0024

    [8] Dyke S J, Spencer B F Jr, Quast P and Sain M K 1995Role of control-structure interaction in protective systemdesign J. Eng. Mech. ASCE121 32238

    [9] Dyke S J, Spencer B F Jr, Quast P, Sain M K, Kaspari DC Jr and Soong T T 1996 Acceleration feedback control

    of MDOF structures J. Eng. Mech. ASCE122 90718[10] Dyke S J, Spencer B F Jr, Quast P, Kaspari D C Jr andSain M K 1996 Implementation of an AMD usingacceleration feedback controlMicrocomput. Civil Eng.11 30523

    [11] Dyke S J, Spencer B F Jr, Sain M K and Carlson J D 1996Seismic response reduction using magnetorheologicaldampers Proc. IFAC World Congress (San Francisco,CA, 1996) pp 14550

    [12] Dyke S J, Spencer B F Jr, Sain M K and Carlson J D 1996Modeling and control of magnetorheological dampersfor seismic response reduction Smart Mater. Struct. 556575

    [13] Dyke S J 1996 Acceleration feedback control strategies foractive and semi-active systems: modeling, algorithmdevelopment and experimental verificationPhD

    Dissertation University of Notre Dame[14] Dyke S J, Spencer B F Jr, Sain M K and Carlson J D 1996Experimental verification of semi-active structuralcontrol strategies using acceleration feedbackProc. 3rdInt. Conf. on Motion and Vibration Control (Chiba,1996) vol 3, pp 2916

    [15] Dyke S J and Spencer B F Jr 1996 Seismic responsecontrol using multiple MR dampers Proc. 2nd Int.Workshop on Structural Control (Hong Kong, 1996)pp 16373

    [16] Fujino Y, Soong T T and Spencer B F Jr 1996 Structurescontrol: basic concepts and applications Proc. ASCEStructural Congress (Chicago, IL) pp 36170

    [17] Gavin H P, Hanson R D and Filisko F E 1996Electrorheological dampers I: analysis and design ASMEJ. Appl. Mech. 63 66975

    [18] Gavin H P, Hanson R D and Filisko F E 1996Electrorheological dampers II: testing and modelingASME J. Appl. Mech. 63 67682

    [19] Ginder J M 1996 Rheology controlled by magnetic fieldsEncyclopedia Appl. Phys.16 487503

    [20] Ginder J M, Davis L C and Elie L D 1996 Rheology ofmagnetorheological fluids: models and measurementsProc. 5th Int. Conf. on ER Fluids, MR Suspensions andAssociated Technology (1995)ed W A Bullough(Singapore: World Scientific) pp 50414

    [21] Housner G W and Masri S F (eds) 1990Proc. US Natl.Workshop on Structural Control Research, University ofSouthern California Publications M9013

    [22] Housner G W and Masri S F (eds) 1993 Proc. Int. Conf. onStructural Control, University of Southern CaliforniaPublications CE-9311

    [23] Housner G W and Masri S F (eds) 1994Proc. 1st Int.Conf. on Structural Control (Pasadena, CA)

    [24] Inaudi J A, Hayen J C and Iwan W D A semi-activedamping brace system J. Eng. Mech. ASCE submitted

    [25] Leitmann G and Reithmeier E 1993 Semiactive control of avibrating system by means of electrorheological fluidsDyn. Control 3 733

    [26] 1994 MATLAB (Natick, MA: MathWorks)[27] Makris N, Burton S A, Hill D and Jordan M 1996 Analysisand design of an ER damper for seismic protection ofstructures J. Eng. Mech. ASCE122 100311

    [28] McClamroch N H and Gavin H P 1995 Closed loopstructural control using electrorheological dampersProc.Am. Control Conf. (Seattle, WA) pp 41737

    [29] Nonami K and Mizuno T 1996Proc. 3rd Int. Conf. onMotion and Vibration Control (Chiba, 1996)

    [30] Soong T T and Constantinou M C (eds) 1994Passive andActive Structural Vibration Control in Civil Engineering(CISM Courses and Lectures 345) (New York: Springer)

    [31] Spencer B F Jr, Dyke S J, Sain M K and Carlson J D 1996Idealized model of a magnetorheological damper Proc.12th Conf. on Analysis and Computation, ASCE(Chicago, IL, 1996) pp 36170

    [32] Spencer B F Jr and Dyke S J 1996 Semi-active structuralcontrol: system identification for synthesis and analysisProc. 1st Eur. Conf. on Structural Control (Barcelona,1996)

    [33] Spencer B F Jr, Dyke S J, Sain M K and Carlson J D 1997Phenomenological model for magnetorheologicaldampers J. Eng. Mech. ASCE123 2308

    [34] Spencer B F Jr 1996 Recent trends in vibration control inthe USA Proc. 3rd Int. Conf. on Motion and VibrationControl (Chiba, 1996) pp K16

    [35] Spencer B F Jr, Dyke S J and Deoskar H S 1997Benchmark problems in structural control, Part I: activemass driver system Earthquake Eng. Struct. Dyn. at press

    [36] Stanway R. Sproston J L and Stevens N G 1987 Non-linearmodelling of an electrorheological vibration damper J.Electrostat.20 167-84

    [37] Quast P, Sain M K, Spencer B F Jr and Dyke S J 1995Microcomputer implementation of digital controlstrategies for structural response reduction Microcomput.Civil Eng. 10 1325

    [38] Yao J T P 1972 Concept of structural control J. Struct. Div.ASCE98 156774

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